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Calculus and Analysis

Differential Equations : Free Fall and Terminal Velocity

An object in free fall in a gravitational field is governed by the ODE m*dv/dt=mg + Fs, where m is the mass of the object, g=9.8 meters/sec is the acceleration of gravity, v(t) is the velocity of the object t seconds after it is released, and Fs denotes external forces acting on the object. In all that follows, assume that v(0)

Chaos : Conjugacy in Discrete Dynamical Systems

I am taking a course in Dynamics/Chaos and I am trying to prove conjugacy between the logistic and quadratic functions. I have some ideas, but cannot get the proof to work. Attached is a word document with the functions and problem.

Intermediate value theorem

Define Intermediate-Value theorem Using this theorem, show that there is a root of P(x)=x^3+x^2+x-1 in the closed interval [0,1].

Discontinuous function conditions

Define a discontinuous function and state the conditions for discontinuity. Find whether the following functions are discontinuous: f(x)=1/x and f(x)=(x)^(1/2) Solve the following:(involves jump discontinuity) A tomato wholesaler finds that the price of newly harvested tomatoes is $16 per pound if he purchases fewer th

Tangent through a point

A portion of a river has the shape of the equation y=1-x^2/4, where distances are measured in tens of kilometres, and the positive y-axis represents due north. the town of Coopers Crossing is situated on the river at its most northerly point. The town of Black Stump is 10 kilometres due south of Coopers Crossing. the town of And

Line Equations : Tangents & Normals

I) Find the equation of the tangent to y=x(1-x) at x=1 ii) Find the equation of the normal to y=x(1-x) at x=1 iii) Find the equations of the tangents to y=x(1-x) that pass through (-1, 1/4)

Differentiability and Limits

Please see the attached file for the fully formatted problems. Let f: I →ℜ where I is an open interval containing the point c, and let k ∈ ℜ. Prove the following 1. f is differentiable at c with f ′(x) = k iff lim h→0 [f(c+h) - f(c)]/h=k 2. If f is differentiable at c with f ′(c) =

Multivariable calculus

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you Sketch the solid bounded by the graphs of the given equation and find its volume by triple integration: z = x^2, y + z = 4, y = 0, z = 0

Multivariable Calculus Functions

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you Sketch the solid bounded by the graphs of the given equation and find its volume by triple integration: z = 10 - x^2 - y^2, y = x^2, x = y^2, z = 0

Multivariable calculus

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you Sketch the solid bounded by the graphs of the given equation and find its volume by triple integration: z = y, y = x^2, y = 4, z = 0

Multivariable Calculus : Radii of Gyration

Find the radii of gyration x and y( x and y have  above them) of the indicated lamina around the coordinate axes: The lamina of the region bounded by y = x^2 and y = 4; (x, y) = y : is the density symbol

Multivariable Calculus : Centroid of a Plane

Find the centroid of the plane region bounded by the given curves. Assume that the density is  = 1 for each region: x = 0, y = 0, x + 2y = 4 : is the density symbol